Claming Planets

By getting enough influence there .. which you get by fighting there

You must send dropships there and join PlanetWars host.
There should be at least planetwars hosts at any time.
You get dropships by playing games there

yes there is planetwars host - at least 2 of them.
If you play you gain dropship.
If you win you gain influence.
If you have enough influence you control planet and can build stuff there or send dropships from there to other nearby planets.

You can also trade influence to buy enough on some plaent to own it or join clan which already has planets.